Question

Which of the following are the correct alternatives regarding standing waves in a string?
A) particles near the antinode have less potential energy than particles near the node when they reach at its extreme position
B) All particles cross their mean position simultaneously
C) Energy and momentum can be transmitted through node
D) Particles which are near antinodes have less kinetic energy than the particles near the node when they cross their mean position.

Answer 1

Hint:-The fact which can be used is the tension near the nodes is minimum while at the antinodes, the tension becomes maximum and all particles perform simple harmonic motion at the same time.

Complete step by step answer:
The standing wave can be defined as the wave which oscillates in time but their peak amplitude profile does not move in space. These waves are also known as stationary waves.

When the string is at the antinode the tension becomes minimum and hence the elongation in the string is minimum, so the potential energy is minimum while at the node, tension is maximum and hence the elongation is also maximum so, the potential energy also becomes maximum. In the standing waves in the string all particles perform the simple harmonic motion with the same time period therefore, the phase difference between any two particles is constant, so they cross the mean position simultaneously.

We know that, node is always at rest, therefore, the energy and momentum cannot be transferred from it. So, option (C) is wrong.

When the particles reach near the anti – node they possess maximum velocity, so the kinetic energy becomes maximum when crossing the mean position. Hence, option (D) is also incorrect.

So, from the above we can conclude that option (A) and (B) are the two correct options.

Note: Nodes can be defined as the locations at which absolute value of amplitude becomes minimum while the anti – nodes can be defined as the locations at which the absolute value of amplitude becomes maximum.